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Enhanced Electrical ImpedanceTomography via the Mumford–Shah Functional

Published online by Cambridge University Press:  15 August 2002

Luca Rondi  and
Fadil Santosa
Luca Rondi
Affiliation:
Institut für Industriemathematik/SFB , Johannes Kepler Universität Linz, Austria. : School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.
Fadil Santosa
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.; santosa@math.umn.edu.
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Abstract

We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several numerical examples. Our results indicate that this is an effective approach for overcoming the illposedness. Moreover, it has the capability of enhancing the reconstruction while at the same time segmenting the conductivity image.

Keywords

Electrical impedance tomographyinverse problems for elliptic equationsregularization of illposed problemimage enhancement.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 517 - 538
Copyright
© EDP Sciences, SMAI, 2001

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